Improved preservation of autocorrelative structure in surrogate data using an initial wavelet step

Keylock, Christopher J.

doi:10.5194/npg-15-435-2008

Cited by 13 publications

(13 citation statements)

References 28 publications

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“…For example, phase synchronisation measures are generally compared to the mean phase synchronisation for several random sorts of the phase data [22], while intermittency and structures in turbulent flows have been evaluated using surrogates that preserve both the histogram of the original data and its spectral properties [3,31]. The computation of such surrogates can be undertaken using Fourier [32] or waveletbased methods [15,16,19]. Given the simple nature of the null hypothesis in this study, the Fourier method (known as the Iterated Amplitude Adjusted Fourier Transform, or IAAFT method) was adopted.…”

Section: Confidence Limits On the Measuresmentioning

confidence: 99%

Evaluating the dimensionality and significance of “active periods” in turbulent environmental flows defined using Lipshitz/Hölder regularity

Keylock

2009

Environ Fluid Mech

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Active periods within perturbed boundary-layer flows are considered in terms of the local roughness of measured velocity time series and defined in terms of Hölder/Lipshitz exponents. Such events are associated with the passage of energetic, coherent flow structures and are responsible for exerting high turbulent stresses because of the rapid changes in velocity that occur at such times. A method is proposed for assessing the effective dimensionality of such active periods, as well as their significance to the flow field, for a particular choice of flow metric. The method is applied to the turbulent flow through a confluence flow geometry, with velocity samples acquired close to the bed of the channel in a zone of complex mixing. The dimensionality of the active periods is consistent with the observed patterns of sediment entrainment from the bed, with the significance of the active periods decaying away from the erosional zone.

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Section: Confidence Limits On the Measuresmentioning

confidence: 99%

Evaluating the dimensionality and significance of “active periods” in turbulent environmental flows defined using Lipshitz/Hölder regularity

Keylock

2009

Environ Fluid Mech

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“…A modified iterated amplitude adjusted Fourier transform (IAAFT) was used to generate a linear surrogate

\overset{C}{true} ((), s)

from a spatial series of curvatures C ( s ) in four steps [see Keylock , , ]. Our procedure for computing curvature series from centerlines is laid out in Appendix A.…”

Section: Is Form Nonlinearity Present In Natural Rivers?mentioning

confidence: 99%

Are process nonlinearities encoded in meandering river planform morphology?

Schwenk

Foufoula‐Georgiou

2017

JGR Earth Surface

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Meandering river planform evolution is driven by the interaction of local nonlinear processes and cutoff dynamics. Despite the known nonlinear dynamics governing the evolution of meandering rivers, previous attempts have found at most a weak signature of these process nonlinearities within the meander planform morphologies (form nonlinearities). In this work, we present a framework to measure form nonlinearity from centerline curvature signals and unambiguously quantify its presence in both a numerically simulated meandering river and three natural rivers. The degree of nonlinearity (DNL) metric is introduced to measure the strength of form nonlinearities embedded in the centerlines. The DNL's evolution through time is computed for annual observations over 30 years of an active, tropical meandering river and for the simulated centerline to understand how cutoffs and bend growths affect form nonlinearity. We find that although cutoffs reduce the overall form nonlinearity, they also act as a source of nonlinearity themselves by creating scales that contribute disproportionately to DNL.

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“…The WiAAFT-procedure follows the iAAFT-algorithm but uses the Maximal Overlap Discrete Wavelet Transform (MODWT) where the iAAFT-procedure is applied to each set of wavelet detail coefficients D j (n) over the dyadic scales 2 j−1 for j = 1, · · · , J, i.e., each set of D j (n) is considered as a time series of its own. The main difference between iAAFT and wiAAFT algorithms is that the former is designed to produce constrained, linear realisations of a process that can be compared with the original time series on some measure, while the later algorithm restricts the possible class of realisations to those that retain some aspect of the local mean and variance of the original time series (Keylock, 2008).…”

Section: Surrogate Data Methods and Statistical Testingmentioning

confidence: 99%

Nonlinear dynamics and recurrence plots for detecting financial crisis

Addo

Billio

Guégan

2013

The North American Journal of Economics and Finance

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Identification of financial bubbles and crisis is a topic of major concern since it is important to prevent collapses that can severely impact nations and economies. Our analysis deals with the use of the recently proposed 'delay vector variance' (DVV) method, which examines local predictability of a signal in the phase space to detect the presence of determinism and nonlinearity in a time series. Optimal embedding parameters used in the DVV analysis are obtained via a differential entropy based method using wavelet-based surrogates. We exploit the concept of recurrence plots to study the stock market to locate hidden patterns, non-stationarity, and to examine the nature of these plots in events of financial crisis. In particular, the recurrence plots are employed to detect and characterize financial cycles. A comprehensive analysis of the feasibility of this approach is provided. We show that our methodology is useful in the diagnosis and detection of financial bubbles, which have significantly impacted economic upheavals in the past few decades.

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Improved preservation of autocorrelative structure in surrogate data using an initial wavelet step

Cited by 13 publications

References 28 publications

Evaluating the dimensionality and significance of “active periods” in turbulent environmental flows defined using Lipshitz/Hölder regularity

Evaluating the dimensionality and significance of “active periods” in turbulent environmental flows defined using Lipshitz/Hölder regularity

Are process nonlinearities encoded in meandering river planform morphology?

Nonlinear dynamics and recurrence plots for detecting financial crisis

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